Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2)

by Emil Artin, Arthur N. Milgram (Editor)

Overview

In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications.
The first section deals with linear algebra, including fields, vector spaces, homogeneous linear equations, determinants, and other topics. A second section considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equations, Jummer's fields, and more.
Dr. Milgram's section on applications discusses solvable groups, permutation groups, solution of equations by radicals, and other concepts.

Product Details

ISBN-13:	9780486623429
Publisher:	Dover Publications
Publication date:	07/10/1997
Series:	Dover Books on Mathematics Series , #2
Pages:	96
Sales rank:	571,372
Product dimensions:	5.50(w) x 8.50(h) x 0.20(d)

Table of Contents

I. Linear Algebra
A. Fields
B. Vector Spaces
C. Homogeneous Linear Equations
D. Dependence and Independence of Vectors
E. Non-homogeneous Linear Equations
F. Determinants
II. Field Theory
A. Extension fields
B. Polynomials
C. Algebraic Elements
D. Splitting fields
E. Unique Decomposition of Polynomials into Irreducible Factors
F. Group Characters
G. Applications and Examples to Theorem 13
H. Normal Extensions
I. Finite Fields
J. Roots of Unity
K. Noether Equations
L. Kimmer's Fields
M. Simple Extensions
N. Existence of a Normal Basis
O. Theorem on natural Irrationalities
III. Applications. By A. N. Milgram
A. Solvable Groups
B. Permutation Groups
C. Solution of Equations by Radicals
D. The General Equation of Degree n
E. Solvable Equations of Prime Degree
F. Ruler and Compass Construction